White - Pips 155
Black - Pips 119
Code:
Cube analysis
Rollout cubeless equity +0,504
Cubeful equities:
1. Double, take +0,759
2. Double, pass +1,000 ( +0,241)
3. No double +0,684 ( -0,075)
Proper cube action: Double, take
The pipdifference is of no importance at all. Decreasing the pipdifference and giving some more flexibility by moving 4w to 19 makes it a no double:
White - Pips 140
Black - Pips 119
Code:
Cube analysis
Rollout cubeless equity +0,320
Cubeful equities:
1. No double +0,436
2. Double, pass +1,000 ( +0,564)
3. Double, take +0,356 ( -0,080)
Proper cube action: No double, take (12,4%)
I approach this problem by outlining methodically the events that can happen after white's turn:
1. black enters
1.1 white gets into the outfield
1.2 white doesn't get into the outfield
2. black does not enter
2.1 white gets into the outfield
2.2 white doesn't get into the outfield
1. black enters
In case black enters on the 22-point, next turn he will almost certainly double white out. This is in 30% of the cases.
After 35 for black, and rather good 52 for white:
Code:
Cube analysis
Rollout cubeless equity +0,631
Cubeful equities:
1. Double, pass +1,000
2. Double, take +1,052 ( +0,052)
3. No double +0,839 ( -0,161)
Proper cube action: Double, pass
So what is left is when black enters on the 24-point.
1.1 white gets into the outfield
There is not very much changed. After 15 for black and 52 for white:
Code:
Cube analysis
Rollout cubeless equity +0,555
Cubeful equities:
1. Double, take +0,868
2. Double, pass +1,000 ( +0,132)
3. No double +0,748 ( -0,120)
Proper cube action: Double, take
This shows that black's situation improves greatly in case he enters. 16 will lead to a pass for white. The probability for this is 3%.
1.2 white doesn't get into the outfield
I presume that white will have a pass. The chance that black throws a 1 is about 30%, and that white doesn't get into the outfield is 45%. That 's in about 15% of the cases.
2. black does not enter
2.1 white gets into the outfield
After 52 for white:
Code:
Cube analysis
Rollout cubeless equity +0,166
Cubeful equities:
1. No double +0,189
2. Double, pass +1,000 ( +0,811)
3. Double, take -0,035 ( -0,224)
Proper cube action: No double, take (21,7%)
There is a considerable equity loss, but the positive thing is that black is still favorite to win. The chance that black will not enter is 45%, and that white skips the 4-prime is 55%. That's in about 25% of the cases.
2.2 white doesn't get into the outfield
11,21,31,32 will lead to a take, and 22,33,44,41,42,43 will lead to a pass. The probability that white throws one of the bad numbers is 25%, which makes 45% x 25% =11%.
Conclusion:
The passes are all market losers. Question is whether the market losses in total are outweighing the no-doubles in total. I have put the percentages of the passes in red and the no-double in green, showing about 60% passes and 25% no-doubles. Taking in account some too positive judgements, there are twice as many passes. Out of simplicity ignoring the strength of the passes and no-doubles, I think this proofs that this position is a double.